Question

Form a polynomial whose zeros and degree are given.
Zeros: 3, multiplicity 1; 2, multiplicity 2; degree 3
Type a polynomial with integer coefficients and a leading coefficient of 1 in the box below.
f(x)=
(Simplify your answer.)

Answer 1

Answer:

$f(x)=x^{3}-7x^{2}+16x-12$

Step-by-step explanation:

we know that

Is a polynomial  of degree 3

The roots are

x=3, multiplicity 1 -----> (x-3)=0

x=2, multiplicity 2 -----> (x-2)(x-2)=0

so

The equation of the polynomial is

$f(x)=a(x-3)(x-2)(x-2)\\\\f(x)=a(x-3)(x-2)^{2}$

The leading coefficient is 1

so

a=1

substitute

$f(x)=(1)(x-3)(x-2)^{2}$

$f(x)=(x-3)(x-2)^{2}$

Convert to expanded form

$f(x)=(x-3)(x^{2}-4x+4)\\\\f(x)=x^{3}-4x^{2}+4x-3x^{2}+12x-12\\\\f(x)=x^{3}-7x^{2}+16x-12$